Recommendation Systems

• Recommendation systems (RS) help to match users with items

• RS are one of the most successful and widespread applications of machine learning technologies in business.

• Content- Based Filtering: Recommeding to user A based on his/her existing profiles.

• Collaborative Filtering: Recommeding to user A based on his/her community's profiles.

• Assume there are four categories of news A) Politics B) Sports C) Entertainment D) Technology

• User A who has read 10 articles related to Technology

• Recommend a new article in Technology for him to read.

• Assume there are four categories of news A) Politics B) Sports C) Entertainment D) Technology

• User A who has read 10 articles related to Technology

• User B who has read the same 10 articles related to Technology and an X article in Sports.

• Recommend the article X to user A.

• Utility Matrix contains ratings of users on items

	Item 1	Item 2	Item 3	Item 4	Item 5
Alice	5	3	4	4	???
User 1	3	1	2	3	3
User 2	4	3	4	3	5
User 3	3	3	1	4	4
User 4	1	5	5	2	1

• A recommendation problem tunrs into a prediction problem.

• Predict the rating of the new user on his/her new item.

• If the predicted rating of Alice on Item 5 are high (4 or 5), we will recommend Item 5 to her.

• A “pure” CF approach and traditional baseline
• Using the utility as inputs
• Returns a ranked list of items based on rating predictions

• Assumptions
  • If users had similar tastes in the past they will have similar tastes in the future
  • User preferences remain stable and consistent over time

	Item 1	Item 2	Item 3	Item 4	Item 5
Alice	5	3	4	4	???
User 1	3	1	2	3	3
User 2	4	3	4	3	5
User 3	3	3	1	4	4
User 4	1	5	5	2	1

• Find find k nearst neighbors of Alice.
• User the average rating of the nearest neighbors on Item 5 as a prediction of Alice on Item 5.

	Item 1	Item 2	Item 3	Item 4	Item 5
Alice	5	3	4	4	???
User 1	3	1	2	3	3
User 2	4	3	4	3	5
User 3	3	3	1	4	4
User 4	1	5	5	2	1

Let \( A1 \) is the distance from Alice to User 1 and so on. We have:

\[ A1 = 3.60 \\ A2 = 1.41 \\ A3 = 3.60 \\ A4 = 5 \]

• For 3NN, the predicted rating of Alice for item 5 is the average of ratings on item 5 of her 3 neast neighbors, User 1, 2 and 3.

• Predicted rating of Alicie on item 5 is: (3+5+4)/3 = 4.

• We will recommend item 5 to Alice.

	Item 1	Item 2	Item 3	Item 4	Item 5
Alice	5	3	4	4	???
User 1	3	1	2	3	3
User 2	4	3	4	3	5
User 3	3	3	1	4	4
User 4	1	5	5	2	1

• Find the k nearest neighbors of Item 5.
• The predicted rating of Alice on item 5 is the average rating of Alice on the nearest neighbors.

	Item 1	Item 2	Item 3	Item 4	Item 5
Alice	5	3	4	4	???
User 1	3	1	2	3	3
User 2	4	3	4	3	5
User 3	3	3	1	4	4
User 4	1	5	5	2	1

Let \( d54 \) be the distance of item 5 to item 4 and so on. We have

\[ d54 = 2.23\\ d53 = 5.19 \\ d52 = 5 \\ d51 = 1.41 \]

• For 3NN, the two nearest neighbors of Item 5 are Item 1,4 and Item 2.

• Predicted rating of Alice on Item 5 is the average of her ratings on Item 1, 4 and 2, which is (5+4+3)/3 = 4

• We recommend her to buy Item 5!

• Neighborhood can be decided by similarity measures
• Similarity can be measured as the inverse of the Distance
• The possible similarity values are between 0 and 1, where values near to 1 indicate a strong similarity.
• There are many distance measure
• There are many similarity measure

• ManhattanDistance between Alice and User 1 (\( A1 \)).

	Item 1	Item 2	Item 3	Item 4
Alice	5	3	4	4
User 1	3	1	2	3

\[ A1 = |5-3| + |3-1|+|4-2|+|4-3| = 7 \]

• Cosine similarity is established as the standard in Recommendation System.

• Cosine similarity between Alice and User 1 (\( S1 \)).

	Item 1	Item 2	Item 3	Item 4
Alice	5	3	4	4
User 1	3	1	2	3

\[ S1 = \frac{5 \cdot 3 + 3 \cdot 1 + 4 \cdot 2 + 4 \cdot 3}{\sqrt{5^2+3^2+4^2+4^2}\cdot \sqrt{3^2+1^2+2^2+3^2}} = 0.975 \]

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